# Financial Calculus

August 26, 2013

Financial Calculus is rather an old book now, first being published in 1996. Despite its age it has (as far as i know) a unique place in the literature in that it attempts to teach continuous time stochastic calculus, without requiring a knowledge of (nor teaching) measure theoretic probability. It does in fact succeed to do this difficult task! By using the binomial tree approach to pricing derivatives it introduces difficult concepts such as measure, risk neutral pricing and change of measure. Ito Calculus is explained using the derivative of $$W_t^2$$ to illustrate that higher order terms are needed in the Taylor expansion in order for the differential to have the right expectation. Using the tools of the Martingale Representation theorem and the Cameron Martin Girsanov Change of Measure theorem the Black Scholes formula is derived. This is quite a feet considering that the word sigma algebra isn’t mentioned once in the book! The later part of the book is devoted to pricing interest rate derivatives. It provides a nice introduction to the Heath Jarrow Morton interest rate model framework  for the forward rate curve but for a detailed approach you should probably look elsewhere. There is also a brief mention of the Libor market model (BJM) but again you should look elsewhere for more details as you could write (and some authors have!) a whole book on the subject.

Rating 4/5

Category: Book Reviews, Stochastic Calculus